1. A giant rolls a bowling ball with a uniform speed of 30 m/s (about 70 mph) ac

Question

1. A giant rolls a bowling ball with a uniform speed of 30 m/s (about 70 mph) across the top of his large desk. The ball rolls off the edge of the desk and lands on the floor 120 m from the edge of the desk. How high is the desk? When the ball has moved a horizontal distance of 60 m how high above the floor is it?

2. A baseball is hit in a line drive and leaves the bat with a horizontal speed of 22 m/s. What are its horizontal and vertical speeds 1/4 s later?

3. You are driving your race car around a circular test track. Which would have a greater effect on the magnitude of your acceleration, doubling your speed or moving to a track with half the radius? Why?

4. An Indy car with a speed of 120 km/h goes around a level, circular track with a radius of 1 km. What is the centripetal acceleration of the car (in m/s2)?

5. The maximum speed with which a 945-kg car makes a 180-degree turn is 10.0 m/s. The radius of the circle through which the car is turning is 25.0 m. Determine the force of friction acting upon the car.

6. A stone tied to a string is being twirled around in uniform circular motion. If the string snaps, what will happen to the stone? Choose from the drawing below its path (represented by one of the arrows) immediately after the string breaks and explain why.

Explanation / Answer

1.

The ball lands 120m from the edge of the desk. So, horizontal distance covered is,

d = 120 m

Horizontal speed is v = 30m/s

So time taken for the ball to reach the floor is,

t = d/v = 120m/(30m/s) = 4s

The initial vertical velocity of the ball was zero. So if the height of the desk is h, then

h = ut + 1/2gt2 = (1/2)gt2 (as u = 0)

or, h = 0.5(9.8 m/s2)(4s)2

or, h = 78.4 m

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Let the ball has moved a horizontal distance of 60m at time t, then

t = 60m/(30m/s)

or, t = 2s

So vertical distance covered in 2s is,

H = (1/2)gt2 = 0.5(9.8m/s2)(2s)2

or, H = 19.6 m

So, the ball's distance from the floor is,

h = 78.4m - 19.6m

or, h = 58.8 m above the floor

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2.

Baseball's horizontal speed 1/4s later is vh = 22 m/s, as there is no horizontal acceleration.

Baseball's vertical speed 1/4s later is vv = u + gt = 0 + 9.8m(1/4s), as initial vertical speed is zero

or, vv = 2.45 m/s

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3.

accelration a = v2/r, so doubling the speed would quadruple the accelration while reducing the radius by half only doubles the acceleration.

So, doubling the speed has greater effect on the magnitude of the acceleration.

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4.

centripetal acceleration is a =  v2/r

v = 120km/h = 33.33 m/s, r = 1km = 1000 m

So, a = v2/r = (33.33 m/s)2/1000 m

or, a = 1.11 m/s2

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5.

centripetal acceleration is a =  v2/r = (10m/s)2/(25 m) = 4m/s2

So centripetal force is F = mv2/r = (945kg)(4m/s2) = 3780 N

This centripetal force is provided by the friction.

So force of friction is f = F = 3780 N

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6.

The direction of velocity of an object under circular motion is always along the tangent to the circle. So when the string snaps, the object flies off along the tangent.

So, correct option is C.

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....

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