Q: A 20 kg sled slides on frictionless ice and then enters a rough patch of snow that exerts a friction force of $$12 \, \mathrm{N}. If $$the sled enters the snow at $$4.0 \, \mathrm{m/s}$$, how far does it travel before coming to rest?

$$d = \dfrac{v^2$}{2a} = \dfrac{(4.0)^2$}{2 \times (12/20)} = 13.3 \, \mathrm{m}$$

Q: A 10 kg block hangs from a rope and is accelerating upward at $$2.5 \, \mathrm{m/s^2$}. $$What is the tension in the rope?

$$T = m(g + a) = 10 \times (9.8 + 2.5) = 123 \, \mathrm{N}$$

Q: A 46 g golf ball is putted at $$3.0 \, \mathrm{m/s}$$ and slows to rest due to a friction force of $$0.020 \, \mathrm{N}. $$How far does the ball travel before stopping?

$$d = \dfrac{v^2$}{2a} = \dfrac{(3.0)^2$}{2 \times (0.020/0.046)} = 10.4 \, \mathrm{m}$$

Q: A 60 kg student stands on a scale in an elevator accelerating upward. The scale reads $$700 \, \mathrm{N}. $$What is the acceleration of the elevator?

$$a = \dfrac{700 - (60 \times 9.8)}{60} = 1.5 \, \mathrm{m/s^2$}$$

Q: A 1500 kg car is towed from rest to $$12 \mathrm{\ m/s} in$$ $$10 \mathrm{\ s} by a $$rope at $$20^\circ$$ above the horizontal. The friction force is $$320 \mathrm{\ N}. $$What is the tension in the rope?

$$T = \dfrac{m a + f}{\cos 20^\circ} = \dfrac{(1500 \times 1.2) + 320}{\cos 20^\circ} = 2100 \mathrm{\ N}$$

Q: A 90 lb astronaut travels to a planet where $$g = 15 \mathrm{\ m/s^2$}. $$What is her mass on that planet?

$$m = 90 \times 0.454 = 40.9 \mathrm{\ kg}$$

Question 1

A 500 N orangutan hangs motionless from a vertical rope. What is the tension in the rope?

Accepted Answer

$$T = 500 \, \mathrm{N}$$

Question 2

A car of mass $$1500 \, \mathrm{kg} is $$being towed at a constant speed by a rope that makes a $$20^\circ$$ angle with the horizontal. If the friction force opposing the motion is $$320 \, \mathrm{N}$$, what is the tension in the rope?

Accepted Answer

$$T = \dfrac{320}{\cos 20^\circ} = 340 \, \mathrm{N}$$

Question 3

Which of the following best describes the condition for an object to be in static equilibrium?

Accepted Answer

The net force on the object is zero and the object is at rest.

Question 4

A 20 kg sled slides on frictionless ice and then enters a rough patch of snow that exerts a friction force of $$12 \, \mathrm{N}. If $$the sled enters the snow at $$4.0 \, \mathrm{m/s}$$, how far does it travel before coming to rest?

Accepted Answer

$$d = \dfrac{v^2$}{2a} = \dfrac{(4.0)^2$}{2 	imes (12/20)} = 13.3 \, \mathrm{m}$$

Question 5

A 70 kg man stands on a scale in an elevator. The scale reads $$750 \, \mathrm{N} as $$the elevator comes to rest. What was the direction of the elevator's motion just before stopping?

Accepted Answer

Downward

Question 6

A 10 kg block hangs from a rope and is accelerating upward at $$2.5 \, \mathrm{m/s^2$}. $$What is the tension in the rope?

Accepted Answer

$$T = m(g + a) = 10 	imes (9.8 + 2.5) = 123 \, \mathrm{N}$$

Question 7

A 46 g golf ball is putted at $$3.0 \, \mathrm{m/s}$$ and slows to rest due to a friction force of $$0.020 \, \mathrm{N}. $$How far does the ball travel before stopping?

Accepted Answer

$$d = \dfrac{v^2$}{2a} = \dfrac{(3.0)^2$}{2 	imes (0.020/0.046)} = 10.4 \, \mathrm{m}$$

Question 8

Which of the following statements about mass and weight is correct?

Accepted Answer

Weight is the gravitational force on an object and depends on location, while mass is constant.

Question 9

A 60 kg student stands on a scale in an elevator accelerating upward. The scale reads $$700 \, \mathrm{N}. $$What is the acceleration of the elevator?

Accepted Answer

$$a = \dfrac{700 - (60 	imes 9.8)}{60} = 1.5 \, \mathrm{m/s^2$}$$

Question 10

A 1000 kg elevator is in free fall after the cable breaks. What does a scale inside the elevator read for a 70 kg person standing on it?

Accepted Answer

$$0 \, \mathrm{N}$$

Question 11

A block is pulled by three forces in the $$xy-$$plane and remains at rest. If two of the forces are $$10 \mathrm{\ N} at$$ $$0^\circ$$ and $$20 \mathrm{\ N} at$$ $$90^\circ$$, what is the magnitude of the third force required for equilibrium?

Accepted Answer

$$F = \sqrt{10^2$ + 20^2$} = 22.4 \mathrm{\ N}$$

Question 12

A 1500 kg car is towed from rest to $$12 \mathrm{\ m/s} in$$ $$10 \mathrm{\ s} by a $$rope at $$20^\circ$$ above the horizontal. The friction force is $$320 \mathrm{\ N}. $$What is the tension in the rope?

Accepted Answer

$$T = \dfrac{m a + f}{\cos 20^\circ} = \dfrac{(1500 	imes 1.2) + 320}{\cos 20^\circ} = 2100 \mathrm{\ N}$$

Question 13

A 50 N object is pulled by a rope at a $$20^\circ$$ angle above the horizontal. What is the tension in the rope if the object is in equilibrium?

Accepted Answer

$$T = 50 \mathrm{\ N}$$

Question 14

Which of the following is the correct expression for the $$y-$$component of a weight vector $$\vec{w} at an $$angle $$	heta$$ below the $$x-$$axis?

Accepted Answer

$$w_y = -w \cos 	heta$$

Question 15

A 90 lb astronaut travels to a planet where $$g = 15 \mathrm{\ m/s^2$}. $$What is her mass on that planet?

Accepted Answer

$$m = 90 	imes 0.454 = 40.9 \mathrm{\ kg}$$

Question 16

A 60 kg student stands on a scale in an elevator that accelerates downward at $$2.0 \mathrm{\ m/s^2$}. $$What does the scale read?

Accepted Answer

$$w_{app} = m(g - a) = 60 	imes (9.8 - 2.0) = 468 \mathrm{\ N}$$

Question 17

A 70 kg astronaut is floating in space, far from any planet. What is her weight?

Accepted Answer

$$w = 0 \mathrm{\ N}$$

Question 18

A 60 kg student in a 1000 kg elevator at rest experiences an apparent weight of $$600 \mathrm{\ N}$$ for the first $$3 \mathrm{\ s} as $$the elevator starts moving. What is the acceleration of the elevator?

Accepted Answer

$$a = \dfrac{600 - (60 	imes 9.8)}{60} = 0.2 \mathrm{\ m/s^2$}$$

L14-15: Applying Newton’s Laws: Equilibrium and Dynamics

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