EXSC 440 Questions with Answers

Austin has a portable basketball goal in his driveway. He has the basket set 8 ft (2.4 m) high so he can practice dunking the ball. He slams the ball through the hoop and then hangs onto the rim. This exerts a downward force of 600 N on the front of the rim. The front of the rim is 1.1 m in front of the front edge of the portable basketball goal's base. The mass of the whole portable basketball goal is 70 kg. The center of gravity of the portable basketball goal is 1.0 m behind the front edge of its base. a. How much torque is produced around the front of the goal base by the 600 N force Austin exerts on the front of the rim? b. How much torque would be needed to tip the goal? c. What is the largest vertical force that can be exerted on the front edge of the rim before the portable basketball goal begins to tip?

a. 660 Nm in counterclockwise direction b. 687 Nm in counter clockwise direction

A baseball pitcher pitches a fastball with a horizontal velocity of 40 m/s. The horizontal distance from the point of release to home plate is 17.50 m. The batter decides to swing the bat 0.30 s after the ball has been released by the pitcher. The average angular velocity of the bat is 12 rad/s. The angular displacement of the bat from the batter's shoulder to hitting positions above the plate is between 1.5 and 1.8 rad. a) Will the bat be in a hitting position above the plate when the ball is above the plate? Assume the pitch is in the strike zone. b)Assume that the batter does hit the ball. If the bat's instantaneous angular velocity is 30 rad/s at the instant of contact, and the distance from the sweet spot on the bat to the axis of rotation is 1.25 m, what is the instantaneous linear velocity of the sweet spot at the instant of ball contact?

b) v = 37.5 m/s v=wr = (30 rad/s)(1.25m)