# Resistive Forces on Objects on an Incline

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1. Aug 17, 2015

### Priyadarshini

1. The problem statement, all variables and given/known data
A boy on a board B slides down a slope. The angle of the slope to the horizontal is 30°. The total resistive force F acting on B is constant.
The boy on the board B moves with velocity v down the slope. The variation with time t of v is shown in Fig. 3.2.

Calculate the resistive force.

2. Relevant equations
wsinA----?

3. The attempt at a solution
Resistive force= WsinA
= 75 x 9.81 x 0.5
= 367.5 N
My answer does not match with the correct answer. How do you solve this?
Thanks!

2. Aug 17, 2015

### SammyS

Staff Emeritus
Use the graph to determine the acceleration.

You didn't include the weight or mass of the boy and board in the problem statement .

What component of the weight is parallel to the incline ?

3. Aug 17, 2015

### Priyadarshini

Oh, I am so sorry! The mass of the boy is 75kg.
The question doesn't say which component of weight is parallel to the incline, but I think it is WsinA.

4. Aug 17, 2015

### SammyS

Staff Emeritus
Find the acceleration.

5. Aug 17, 2015

### Priyadarshini

a=(v-u)/t
a= 7.4/ 2.5 (the question asks us to calculate all the answers till 2.5s)
= 2.96 m/s^2
But then what? Do I use F=ma? With this formula the answer comes to 222N, but the answer is 147N.

6. Aug 17, 2015

### SammyS

Staff Emeritus
What are you using for the net force?

Show your work.

7. Aug 17, 2015

### Priyadarshini

I multiplied the acceleration I found with the mass of the boy:
F=75 x 2.96
= 222 N
Is this the net force or the force that opposes the boy?

8. Aug 17, 2015

### SammyS

Staff Emeritus
That's the net force required for the boy and board to have an acceleration of 2.96m/s2.

What two forces combine to make that net force?

9. Aug 17, 2015

### Priyadarshini

The resistive force opposing the horizontal component of weight and the contact force?

10. Aug 17, 2015

### SammyS

Staff Emeritus
Yes for the resistive force. No for the contact force.

What does W⋅sin(A) result from? You seem to have abandoned it .

11. Aug 17, 2015

### Priyadarshini

W sin A results from the weight of the boy, which is a force.
So the weight of the boy + the resistive force= the net force?
Then,
The resistive force= 222-367.5
=-145.5
On rounding off to 2 sf, it gives 150N, just like in the answer!
Thanks!

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