Question

13-7. The 10-lb block has a speed of 4 ft/s when the force of F = (8t^2) lb is applied. Determine the velocity of the block when it moves s = 30 ft. The coefficient of kinetic friction at the surface is mus = 0.2.

Answer 1

Concepts and reason

Kinematics:

If the velocity or position of the particle is to be found, it will be necessary to apply the necessary kinematics equations once the particle’s acceleration is determined from the equation,

Friction:

If a moving particle contacts a rough surface, it may be necessary to use the frictional equation, which relates the frictional and normal forces and N acting at the surface of the contact by using the coefficient of kinetic friction, .

Remember that always acts on the free body diagram such that it opposes the motion of the particle relative to the surface it contacts. If the particle is on the verge of relative motion, then the coefficient of static friction is used.

Fundamentals

A body is in equilibrium if vector sum of all the forces is equal to zero or moment of all force vectors about any point is equal to zero.

If the velocity or position of the particle is to be found, it will be necessary to apply the necessary kinematics equations once the particle’s acceleration is determined from the equation,

If acceleration is a function of time, use $a=dv/dt $ and $v=ds/dt $which, when integrated, yield the particles velocity and position.

General sign convection for moment: The moment is considered positive in counter-clockwise direction and negative in clockwise direction.

General sign convection for axis: Distance along the axis is positive and opposite to the axis is negative.

Draw free body diagram of the block.

Apply force equilibrium in the vertical direction.

Here, is the normal reaction acting on the block in vertical direction, W is the weight of the block, m is the mass of the block, is the acceleration due to gravity and is the acceleration of the block in the vertical direction.

The block moves in the horizontal direction. Therefore, the acceleration in the vertical direction becomes zero.

Substitute 10 lb for W, 0 for , and for .

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Apply force equilibrium in the horizontal direction.

Here, is the external force applied on the block, is the frictional force acting between the block and the ground, t is the time of application of the force, is the static friction of coefficient and is the acceleration of the block in the horizontal direction.

Substitute 10 lb for W, 10 lb for N, 0.2 for , and for .

The velocity of the block can be calculated by integrating the velocity equation.

$dv=adt $

Substitute for and integrate the equation between the limits.

The displacement of the block can be calculated by integrating the velocity equation.

Substitute for and integrate the equation between the limits.

Substitute 30 ft for s and solve the equation for the value of t.

Calculate the velocity of the block at s =30 ft using equation (1).

Substitute 2.0089 s for t.

Ans:

The velocity of block is

Answer 2

it would be in ft/s idiot