Forces & Newton s Laws FR Practice Problems

Transcription

1 1) A drag-racing car speeds up from rest to 22 m/s in 2 s. The car has mass 800 kg; the driver has mass 80 kg. a) Calculate the acceleration of the car. b) Calculate the net force on the car. c) Which experiences a greater net force: the driver, the car, or neither? 2) A 7 N block sits on a rough surface. It is being pulled by a force F 1 at an angle θ = 30 above the horizontal, as shown above. The block is initially moving to the right with speed 5 m/s. The coefficient of friction between the block and the surface µ = Is it possible for the block to be slowing down? If so, give a value for the magnitude F 1 that would allow the block to slow down. If not, explain why not with reference to Newton s second law.

2 3) Bert, Ernie, and Oscar are discussing the gas mileage of cars. Specifically, they are wondering whether a car gets better mileage on a city street or on a freeway. All agree (correctly) that the gas mileage of a car depends on the force that is produced the car gets fewer miles per gallon if the engine must produce more force. Whose explanation is completely correct? Bert says: Gas mileage is better on the freeway. In town the car is always speeding up and slowing down because of the the traffic lights, so because F = ma and acceleration is large, the engine must produce a lot of force. However, on the freeway, the car moves with constant velocity, and acceleration is zero. So the engine produce, allowing for better gas mileage. Ernie says: Gas mileage is better in town. In town, the speed of the car is slower than the speed on the freeway. Acceleration is velocity divided by time, so the acceleration in town is smaller. Because F = ma, then, the force of the engine is smaller in town giving better gas mileage.

3 Oscar says: Gas mileage is better on the freeway. The force of the engine only has to be enough to equal the force of air resistance the engine doesn t have to accelerate the car because the car maintains a constant speed. Whereas in town, the force of the engine must often be greater than the force of friction and air resistance in order to let the car speed up. 4) A skydiver is falling with speed v 0 through the air. At the moment (t = o) she opens her parachute and experiences the force of air resistance whose strength is given by the equation F = kv, in which k is a proportionality constant, and v is the speed of descent. The total mass of the skydiver and equipment is m. Assume g is constant throughout her descent. a) Draw and label all the forces acting on the skydiver after her parachute. b) Determine the skydiver s acceleration in terms of m, v, k and g. c) Determine the skydiver s terminal speed (that is, the eventual constant speed of descent). d) Sketch a graph of v as a function of time, being sure to label important values on the vertical axis.

4 5) This question concerns the motion of a crate being pulled across a horizontal floor by a rope. In the diagram below, the mass of the crate is m, the coefficient of kinetic friction between the crate and the floor is µ and the tension in the rope is F T. a) Draw and label all the forces acting on the crate. b) Compute the normal force acting on the crate in terms of m, F T, θ, and g. c) Compute the acceleration of the crate in terms of m, F T, θ, µ and g.

5 6) A force is applied at an angle θ below the horizontal to a mass m resting on a horizontal surface where the coefficients of friction are µ S and µ k. The magnitude of F is slowly increased until the mass just starts to move. At this point, the acceleration is a 0. Calculate the following in terms of µ S and µ k, θ, m, and g. a) Determine the value of F where movement just begins. b) Determine a 0.

6 7) In the diagram below, a massless string connects two blocks of mass m 1 and m 2, respectively on a flat, frictionless tabletop. A force F pulls on Block #2, as shown: a) Draw and label all of the forces acting on Block #1. b) Draw and label all of the forces acting on Block #2. c) What is the acceleration of Block #1? State your answer in terms of F, m 1, and m 2. d) What is the tension connecting the two blocks? State your answer in terms of F, m 1, and m 2. e) If the connecting string connecting the bocks were not massless, but instead had a mass m, figure out (i) the acceleration of Block #1, in terms of F, m, m 1, and m 2. (ii) the difference between the strength of the force that the connecting string exerts on Block #2 and the strength of the force that the connecting string exerts on Bock #1. Please state your answer in terms of F, m, m 1, and m 2.

7 8) A 3 kg block is placed on top of a 7 kg block as shown below. The coefficient of kinetic friction between the 7 kg block and the surface is A horizontal force F acts on the 7 kg block. a) Draw a free-body diagram for each block. b) Calculate the magnitude of the applied force F necessary to maintain an acceleration of 5 m/s 2. c) Find the minimum coefficient of static friction necessary to prevent the 3 kg block from slipping.

8 9) A 10 kg box slides down a plane inclined at an angle (θ = 30 ). The plane has a coefficient of friction (µ = 0.1). The box starts from rest and slides down the plane for 2 s. a) Draw a free-body diagram of this situation, and label all the forces on the box. b) Calculate the force of friction on the box. c) Calculate the acceleration of the box. d) Calculate the final velocity of the box. e) Calculate the distance that the box moves down the plane in the given time interval.

9 10) A 1.5 kg block is placed at the top of a 38 inclined plane at 3.8 m/s 2. a) Draw the forces acting on the block as it moves down the plane. b) Write an equation to determine the coefficient of friction between the block and the plane as the block accelerates down the plane. Calculate the coefficient of friction. c) Some time later, the block is pushed up the plane by a push P, of 16 N, applied to the body and directed upward and parallel to the plane. The friction acting between the plane and the 1.5 kg block is greater than the friction acting when the block accelerated down the plane the same as the friction acting when the block accelerated down the plane less than the friction acting when the block accelerated down the plane

10 11) In the diagram, the 8 kg mass moves up the incline, where the coefficient of ki netic friction is 0.4. Assume an ideal pulley. a) Determine the friction force acting on the 8 kg mass. b) Determine the acceleration of each mass. c) Determine the tension in the connecting rope.

11 12) In the figure shown, assume that the pulley is frictionless and massless. a) If the surface of the inclined plane is frictionless, determine what values of θ will cause the box of mass m 1 to (i) (ii) accelerate up the ramp slide up the ramp at a constant speed b) If the coefficient of kinetic friction between the surface of the inclined plane and the box of mass m, is µ, derive (but do not solve) an equation satisfied by the value of θ which will cause the mass m to slide up the ramp at a constant speed.

12 13) In a laboratory experiment the acceleration of a small cart is measured by the separation of dots burned at regular intervals onto paraffin-coated tape. Weights are transferred from the small cart that is connected by a massless cord to a weight hanger that passes over a frictionless pulley. The surface is considered frictionless, thus the weight at the end of the cord is the resultant force on the system. Students obtained the following data: a) Plot the graph of force versus acceleration on the grid below.

13 b) What is the slope of the graph, and what is its significance? c) Why did students in this experiment transfer weights from the small cart to the weight hanger attached to the cord? Explain your answer using the correct scientific terms.

14 14) Two metal guide rails for a 450 kg mine elevator each exert a constant frictional force of N on the elevator car when it is moving upward with an acceleration of 2.5 m/s2, as shown in the diagram below. Attached to the lower right side of the cable lifting the elevator is a counterweight of mass M. The pulley is an ideal pulley. a) What is the direction of the net force on the elevator car?

15 b) On the elevator cage represented below, sketch and clearly label all forces acting on the elevator during its motion. c) What is the tension in the supporting cable when the elevator is accelerating as described? d) Explain using the correct scientific terms and without writing a mathematical equation how you would determine the mass M of the counterweight needed to give the elevator cage the described acceleration.

16 15) When you and your lab partners enter the physics classroom, your teacher has laboratory equipment on the tables and asks you to determine what, if any, relationship exists between a constant force and a variable mass. a) Design a laboratory experiment in enough detail that another student could duplicate your results and reach the same conclusion(s) about your inquiry lab. b) Make a sketch of your equipment, and correctly label each part of the sketch. c) What measurements will you take and how will you use them to answer your experimental question?

17 d) Another group of students obtained data to plot the graph below. How does this graph answer the experimental question?