Question

1. a.) Suppose a hockey puck slides down a frictionless ramp with an acceleration of 5 m/s². What angle does the ramp make with respect to the horizontal?

b) If the ramp has a length of 6 m, how long does it take the puck to reach the bottom?

c) Now suppose the mass of the puck is doubled, What will be it’s acceleration?

2. A space-walking astronaut of total mass 148 kg exerts a force of 265 N on a free-floating satellite of mass 635 kg, pushing it in the +x direction.

a. What is the reaction force exerted by the satellite on the astronaut?

b. Calculate the acceleration of the astronaut

c.The acceleration of the satellite

Answer 1

Explanations & Calculations

1.a)

• Acceleration on a frictionless incline is given by $\small a = g\sin\theta$, so using this we get the following.

$\qquad\qquad \begin{aligned} \small 5\,ms^{-2}&=\small 9.8\,ms^{-2}\times\sin\theta\\ \small \theta&=\small 30.7^0 \end{aligned}$

b)

• Use $\small s = ut+1/2 at^2$ along the incline downward.

$\qquad\qquad \begin{aligned} \small 6\,m&=\small 0+\frac{1}{2}\times5\,ms^{-2}\times t^2\\ \small t&=\small 1.5\,s \end{aligned}$

c)

• The acceleration does not depend on mass so it remains unchanged.

2.a)

• It is equal to the applied force of 265 N as it is the only force that exists in the given scenario.

b)

$\qquad\qquad \begin{aligned} \small F&=\small ma\\ \small a&=\small \frac{265\,N}{148\,kg}=1.8\,ms^{-2} \end{aligned}$

c)

$\qquad\qquad \begin{aligned} \small F&=\small ma\\ \small a&=\small \frac{265\,N}{635\,kg}=0.4\,ms^{-2} \end{aligned}$