COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 2, Problem 87P

(a)

To determine

The magnitude of the force F holding the ball.

(a)

Expert Solution
Check Mark

Answer to Problem 87P

The magnitude of the force F holding the ball is 34 N .

Explanation of Solution

The free body diagram of the system is shown in figure 1.

COLLEGE PHYSICS-CONNECT ACCESS, Chapter 2, Problem 87P

Since the ball is held in its position, it will be in equilibrium so that the net force on it along horizontal and vertical directions will be zero.

Write the equation for the net force along y direction.

  ΣFy=0        (I)

Here, ΣFy is the net force on the ball along y direction.

Write the expression for ΣFy .

  ΣFy=Ty+W        (II)

Here, W is the gravitational force and Ty is the y component of the tension in the string.

Write the expression for W .

  W=mg

Here, m is the mass of the ball and g is the acceleration due to gravity.

Write the expression for Ty .

  Ty=Tsinθ

Here, T is the tension in the string and θ is the angle the string makes with the horizontal.

Put the above two equations in equation (II).

  ΣFy=Tsinθ+(mg)=Tsinθmg

Put the above equation in equation (I).

Tsinθmg=0T=mgsinθ        (III)

Write the equation for the net force along x direction.

  ΣFx=0        (IV)

Here, ΣFx is the net force on the crate along x direction.

Write the expression for ΣFx .

  ΣFx=F+Tx        (V)

Here, F is the magnitude of the force holding the ball and Tx is the x component of the tension.

Write the expression for Tx .

  Tx=Tcosθ

Put the above equation in equation (V).

  ΣFx=F+(Tcosθ)=FTcosθ

Put the above equation in equation (IV).

  FTcosθ=0F=Tcosθ        (VI)

Conclusion:

The value of g is 9.80 m/s2 .

Substitute 2.0 kg for m , 9.80 m/s2 for g and 30° for θ in equation (III) to find T .

  T=(2.0 kg)(9.80 m/s2)sin30°=39.2 N

Substitute 39.2 N for T and 30° for θ in equation (VI) to find F .

  F=(39.2 N)cos30°=34 N

Therefore, the magnitude of the force F holding the ball is 34 N .

(b)

To determine

The tension in the string.

(b)

Expert Solution
Check Mark

Answer to Problem 87P

The tension in the string is 39 N .

Explanation of Solution

Equation (III) can be used to determine the tension in the string.

Conclusion:

Substitute 2.0 kg for m , 9.80 m/s2 for g and 30° for θ in equation (III) to find T .

  T=(2.0 kg)(9.80 m/s2)sin30°=39.2 N39 N

Therefore, the tension in the string is 39 N .

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Chapter 2 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

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