Analytical method of vector addition

[cDamann]

Homework Statement

Joe pushes on the handle of a 10 kg lawn spreader. The handle makes a 45° angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5s. What force must Joe apply to the handle? Neglect friction.

Homework Equations

A=Vf-Vi/t. F=ma

The Attempt at a Solution

i calculated the acceleration being 1.39-0/1.5= 0.927m/s squared.
i honestly don't know what to do next, please help.

 

[SammyS]

Homework Statement

Joe pushes on the handle of a 10 kg lawn spreader. The handle makes a 45° angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5s. What force must Joe apply to the handle? Neglect friction.

Homework Equations

A=Vf-Vi/t. F=ma

The Attempt at a Solution

i calculated the acceleration being 1.39-0/1.5= 0.927m/s squared.
i honestly don't know what to do next, please help.

What is the direction that acceleration must have?

 

[cDamann]

looking at a free body diagram on the page of the lawn spreader, the acceleration is going →.

 

[SammyS]

looking at a free body diagram on the page of the lawn spreader, the acceleration is going →.

Correct.

So the horizontal component of the force must be able to produce that acceleration.

 

[Nickie]

I would approach this problem by using the analytical method of vector addition. This method involves breaking the forces into their horizontal and vertical components, and then adding them together to find the resultant force.

First, we need to find the horizontal and vertical components of the force that Joe is applying to the handle. The horizontal component can be found by multiplying the magnitude of the force by the cosine of the angle (45°). This would give us Fx = Fcos(45°). Similarly, the vertical component can be found by multiplying the magnitude of the force by the sine of the angle (45°). This would give us Fy = Fsin(45°).

Next, we can use the equation F=ma to find the magnitude of the force needed to accelerate the spreader at 0.927m/s^2. This would give us F = m*a = (10kg)*(0.927m/s^2) = 9.27N.

Now, using the Pythagorean theorem, we can find the magnitude of the total force needed by adding the horizontal and vertical components together. This would give us F = √(Fx^2 + Fy^2) = √(9.27^2 + 9.27^2) = 13.13N.

Therefore, Joe needs to apply a force of 13.13N at a 45° angle with the horizontal to accelerate the spreader from rest to 1.39 m/s in 1.5s. It is important to note that this is the minimum force needed, as it assumes no friction. In real life, Joe may need to apply a slightly greater force to overcome the effects of friction.