Q: A gondola basket is supported by two cables at an angle $$\theta$$ from the horizontal. If the total weight is $$W$$, what is the tension $$T in $$each cable?

$$T = \dfrac{W}{2 \sin \theta}$$

Question 1

A robot moves east at a speed of $$2\ \mathrm{m/s}$$, while another robot moves $$35^\circ$$ north of west at a speed of $$1.8\ \mathrm{m/s}. $$What is the magnitude of the velocity of the second robot relative to the first?

Accepted Answer

$$2.1\ \mathrm{m/s}$$

Question 2

You set up a ramp for your robot at $$23^\circ$$ above the horizontal. After driving off the ramp, the robot reaches the highest point in its trajectory after $$0.1\ \mathrm{s}. $$What was the speed with which it left the ramp? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.6\ \mathrm{m/s}$$

Question 3

A gondola basket is held up by two cables at an angle $$	heta = 70^\circ$$ from the horizontal. If the total weight of the gondola and passengers is $$5000\ \mathrm{N}$$, what is the maximum tension in each cable?

Accepted Answer

$$2655\ \mathrm{N}$$

Question 4

A cart of mass $$4000\ \mathrm{kg} is $$pulled by a force $$F_T to $$the side, and a mechanical arm applies a force $$F_P = 1800\ \mathrm{N}$$ perpendicular to $$F_T to $$accelerate the cart at $$0.8\ \mathrm{m/s^2$}. $$What is the magnitude of the net force on the cart?

Accepted Answer

$$3200\ \mathrm{N}$$

Question 5

A tension force $$F_T is $$applied at a $$30^\circ$$ angle above the horizontal to a ride in a children's park. If the acceleration is $$0.8\ \mathrm{m/s^2$}$$ and the mass is $$4000\ \mathrm{kg}$$, what is the magnitude of $$F_T$$?

Accepted Answer

$$3692\ \mathrm{N}$$

Question 6

A hockey puck is held $$0.8\ \mathrm{m}$$ above the ice and slides forward at $$v = 1\ \mathrm{m/s}$$ before being dropped. How far will it travel horizontally before hitting the ice? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$0.36\ \mathrm{m}$$

Question 7

You want to pass a puck to a teammate $$2.3\ \mathrm{m}$$ from the boards, and you are $$4.1\ \mathrm{m}$$ from your teammate. At what angle $$	heta$$ should you strike the boards so the puck reaches your teammate?

Accepted Answer

$$56^\circ$$

Question 8

A puck is received at $$6.5\ \mathrm{m/s}$$ and then accelerates at $$2.1\ \mathrm{m/s^2$}$$ for $$4.8\ \mathrm{m} to $$reach a teammate. What is the final speed of the puck?

Accepted Answer

$$8.7\ \mathrm{m/s}$$

Question 9

Which of the following best describes the vector addition needed to find the velocity of one robot relative to another?

Accepted Answer

Subtract the velocity vector of the reference robot from the other robot's velocity vector.

Question 10

A mechanical arm applies a force perpendicular to the direction of motion of a cart. What is the effect on the cart's velocity?

Accepted Answer

It changes the direction but not the speed.

Question 11

If a tension force is applied at an angle to a mass, which component is responsible for accelerating the mass horizontally?

Accepted Answer

The horizontal component of the tension force.

Question 12

A robot moves with velocity $$\vec{v}_1$$ and another with $$\vec{v}_2. $$The velocity of the second robot relative to the first is given by:

Accepted Answer

$$\vec{v}_2 - \vec{v}_1$$

Question 13

A gondola basket is supported by two cables at an angle $$	heta$$ from the horizontal. If the total weight is $$W$$, what is the tension $$T in $$each cable?

Accepted Answer

$$T = \dfrac{W}{2 \sin 	heta}$$

Question 14

A puck is dropped from a height $$h$$ and moves horizontally at speed $$v. $$The time to hit the ground is:

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 15

A cart of mass $$m is $$accelerated at $$a by a $$net force $$F. $$Which equation correctly relates these quantities?

Accepted Answer

$$F = m a$$

Question 16

A force $$F is $$applied at an angle $$	heta to $$the direction of motion. What is the horizontal component of the force?

Accepted Answer

$$F \cos 	heta$$

Question 17

A puck is passed off the boards at an angle $$	heta$$ and travels a distance $$d to a $$teammate. Which trigonometric function relates $$d$$ and $$	heta if $$the horizontal distance is $$x$$?

Accepted Answer

$$\cos 	heta = \dfrac{x}{d}$$

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