Explanation Given data: A spring is clamped to the table. The spring shoots a 20 g ball horizontally. Mass of the ball ( m ) is 20 g, which is written as 0.02 kg. The compressed length of the spring ( Δ x ) is 20 cm. When the spring is compressed, the ball travels horizontally 5.0 m and lands on the floor 1.5 m below the point at which it left the spring. Formula used: The time taken by the ball in vertical motion is equal to the horizontal motion by the second equation of motion. Write the expression for second equation of motion of the ball as follows. y = u y t + 1 2 g t 2 (1) Here, y is the vertical distance from the floor to the point at which it left the spring, which is given as 1.5 m, u y is the initial velocity of the ball when it starts falling to the floor, which is 0 m s since the ball falls at rest, t is the time taken by the ball to fall from the spring position to the floor, and g is the acceleration due to the gravity, which is 9.8 m s 2 . Write the expression for kinetic energy. K = 1 2 m v 2 (2) Here, m is the mass of the ball, and v is the velocity (speed) of the ball. Write the expression for elastic potential energy (potential energy stored in the spring). U s = 1 2 k ( Δ x ) 2 (3) Here, k is the spring constant, and Δ x is the compression length of the spring. Explanation: Calculation of time taken by the ball for its horizontal motion ( t ) : Substitute 1.5 m for y , 0 m s for u y , and 9.8 m s 2 for g in equation (1), 1.5 m = ( 0 m s ) t + 1 2 ( 9.8 m s 2 ) t 2 Simplify the expression to find the time taken by the ball for its horizontal motion as follows. t = 2 ( 1.5 m ) 9.8 m s 2 = 0.3061 s 2 = 0.5532 s Calculation of velocity of the ball in its horizontal motion: Write the expression for velocity of the ball in its horizontal motion as follows. v x = x t (4) Here. x is the horizontal distance travelled by the ball on the table, which is 5.0 m. Substitute 5.0 m for x , and 0.5532 s for t in equation (4), v x = 5.0 m 0.5532 s = 9.0383 m s Calculation of kinetic energy of the ball in its horizontal motion: Modify the expression in equation (2) for the kinetic energy of the ball its horizontal motion as follows

Pearson eText for College Physics: A Strategic Approach -- Instant Access (Pearson+)

4th Edition

ISBN: 9780137561520

Author: Randall Knight, Brian Jones

Publisher: PEARSON+

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Chapter 10, Problem 80GP

To determine

To find: The spring constant of the spring.

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Chapter 10, Problem 79GP

Chapter 10, Problem 81GP

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Pearson eText for College Physics: A Strategic Approach -- Instant Access (Pearson+)

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