A pendulum consists of a 1.7-kg bob attached to a light 2.1-m-long string. While

Question

A pendulum consists of a 1.7-kg bob attached to a light 2.1-m-long string. While hanging at rest with the string vertical, the bob is struck a sharp horizontal blow, giving it a horizontal velocity of 5.0 m/s. At the instant the string makes an angle of 21° with the vertical, calculate the following:

(a) The speed : This is what I need most of all. The last answer I enetered, 1.65m/s, was wrong.

(b) the gravitational potential energy (relative to its value is at the lowest point) : I already have this. The correct answer is 2.32J.

(c) the tension in the string: The last entered answer was 15.55N which was wrong because (a) was wrong. I'm not sure that the formula was correct either. Is this the right one? : T = ( mv'^2 / L ) + mg cos

Explanation / Answer

a) Here ,

let the speed at this instant is v

Using conservation of energy

0.5 * m * v^2 = 0.5 * m * 5^2 - m * 9.8 * 2.1 * ( 1 - cos(21))

0.5 * v^2 = 0.5 * 5^2 - 9.8 * 2.1 * ( 1 - cos(21))

solving for v

v = 4.72 m/s

the speed at this instant is 4.72 m/s

b)

gravitational potential energy = m * 9.8 * 2.1 * ( 1 - cos(21))

gravitational potential energy = 1.7 * 9.8 * 2.1 * ( 1 - cos(21))

gravitational potential energy = 2.32 J

c)

T = mv^2/l + mg * cos(theta)

T = 1.7 *(4.72^2/2.1 + 9.8 * cos(21))

T = 33.6 N

the tension is 33.6 N

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