F FA ACULTY C U L T Y OF O F EDUCATION E D U C A T I O N Departent of Curriculu and Pedagogy Physics Dynaics: Forces Science and Matheatics Education Research Group Supported by UBC Teaching and Learning Enhanceent Fund 2012-2013
Question Blocks Title a Pyraid
Question Title Blocks on a Pyraid I A block is at rest on the rough surface of a pyraid. What is the noral force acting on the block if its ass is 1 and the slope is degrees? A. 1 g B. 1 gsin C. 1 gcos D. 1 E. No idea
Coents Solution Answer: C Justification: Fro a free body diagra of the block (shown below), we see that the noral force ust be equal to the y- coponent of the force due to gravity, in order to aintain a net force along the y-axis of 0. +y N f g y is adjacent to the angle, so: g y = 1 gcos 1 g g y g x
Question Title Blocks on a Pyraid II If the coefficient of friction is μ, what is the net force acting on the block? A. 1 g B. 1 g(μcos - sin) C. 1 g(sin + μcos) D. 1 gsin +y E. No idea
Coents Solution Answer: B Justification: Using the free body diagra in the last question, we see that the force acting on the block is ostly contributed by the coponent of gravity parallel to the rap (since the perpendicular coponent is cancelled by the noral force), which has a value of 1 gsin. The noral force is 1 gcos and the coefficient of friction is μ, giving a friction force of μ 1 gcos. +y The friction force and gravity force are in opposite directions, with the friction force pointing in the positive x direction. F net = 1 g(μcos sin) Notice, since the block is at rest, we are talking About static friction and μ s. N 1 g f g y g x
Question Title Blocks on a Pyraid III Here we have the sae situation except there are now two asses connected by a wire and a pulley. The angles and coefficients of friction are the sae. If 1 > 2, what would be the net force on 1? A. F g1x B. F g1 sin F fric1 +y C. F g1 sin - F fric1 - F g2 + F fric2 D. F g1 sin F fric1 F g2 F fric2 E. No idea
Coents Solution Answer: D Justification: The inforation 1 >> 2 eans that the 1 will go down the rap while 2 will go up the rap. Thus, the forces on block 1 due to gravity and friction oppose each other, while the forces of gravity and friction on 2 will be directed in the sae direction. The forces on block 2 are in the sae direction, because friction always opposes the direction of otion. The forces of tension T are the sae on both blocks as they are connected by the sae string. +y T T f 1 Fg 1 f 2 Fg 2
Question Title Blocks on a Pyraid IV Here we have the sae situation except there are now two asses connected by a wire and a pulley. The angles and coefficients of friction are the sae. If 1 > 2, what would be the agnitude of the net force on 1? A. 1 g B. 1 g(sin - μcos) C. 1 g(sin - μcos) - 2 g(sin - μcos) D. 1 g(sin - μcos) - 2 g(sin + μcos) E. No idea
Coents Solution Answer: D Justification: The force going forward is 1 gsin (gravity on 1 ), while the three forces opposing it are μ 1 gcos (friction on 1 ), 2 gcos (gravity on 2 ), and μ 2 gcos (friction on 2 ). The signs in front of the three forces opposing the gravity on 1 are all negative, but since 2 is taken out of the brackets along with the negative sign in front of it, D is the correct answer. 1 gsin - μ 1 gcos - 2 gcos - μ 2 gcos = 1 g(sin μcos) - 2 g(cos + μcos) +y T f 1 T Fg 1 f 2 Fg 2
Question Title Blocks on a Pyraid V There are two asses connected by a wire and pulley resting on a pyraid. The angles and coefficients of friction are the sae. If 2 > 1, what would be the agnitude of the net force on 1? A. F g2 sin B. F g2 sin F fric2 C. F g2 sin F fric2 F g1 + F fric1 D. F g2 sin F fric2 F g1 F fric1 E. No idea
Coents Solution Answer: D Justification: This is essentially the sae question as nuber 3, except the roles of 1 and 2 are reversed. Friction always opposes The direction of the positive x- axis has also been reversed.
Question Title Blocks on a Pyraid VI There are two asses connected by a wire and pulley resting on a pyraid. The angles and coefficients of friction are the sae. What is the axiu value of 2 that allows the asses to stay still? A. tan B. 2 g( ) C. D. E. None of the above 1
Coents Solution Answer: C Justification: We only need to consider the case of 2 > 1 because it asks for the axiu value of 2 1 The contraption will be at rest if the driving force is less than or equal to the opposing forces: 2 gsin μ 1 gcos + 1 gsin + μ 2 gcos. Regrouping, we find that this is true if 2 (sin - μcos) 1 (sin + μcos). Therefore, 2 1
Question Title Blocks on a Pyraid VII There are two asses connected by a wire and pulley resting on a pyraid. The angles and coefficients of friction are the sae. What is the iniu value of 1 that allows the 2 asses to stay still? A. tan B. 2 g( ) C. D. E. None of the above
Coents Solution Answer: D Justification: This is siply a reversal of question 5, except this tie 1 is the doinant block. Because the syste is syetric, for 1 > 2, 1 2 (reverse the roles of 1 and 2 in question 5). We then find the answer by siply taking the reciprocal (while noting the greater than sign reverses). 1 2