# How do you find frictional force with no mass given?

• KingPhysics
In summary, the conversation discusses how to calculate the force needed for the Batmobile's engine to accelerate at 0.60g down a hill with a 30 degree incline and a coefficient of kinetic friction of 0.28. The conversation includes different attempts at solving the problem and clarifies that the mass of the Batmobile should not be assumed to be 0.6 kg. The final solution is Fengine = 3.37m N, where m is the mass of the Batmobile.
KingPhysics

## Homework Statement

Batman is driving the Batmobile down a hill coming from the Bat Cave. This hill is inclined at an angle of 30 degrees to the horizontal and has a coefficient of kinetic friction of 0.28. What force must the Batmobile's engine apply to cause the Batmobile to accelerate at 0.60g?

a = 0.60g = 0.60(9.8) = 5.88
uk = 0.28

## Homework Equations

Fengine = ma + mg sin30 + Ff

## The Attempt at a Solution

I tried plugging in what I had into the above equation, assuming that the mass was 0.60, so I got Fengine = (0.6)(5.88) + (0.6)(9.8)sin30 + 1.64 and my answer was 8.1 N as the force applied on the engine. But when I looked at the back of the book, it said that the answer is (3.36)(mass) N. How does that work? I am so confused!

0.6 kg is about the weight of five apples, whereas the Batmobile is the size of a tank. How can you assume that m is 0.6 kg? Just call it "m" and assume it's known.

First, draw a free-body diagram of the Batmobile. Remember to label all forces. Then write Newton's second law for the direction parallel to the ramp and the direction perpendicular to it.

I'm also quite interested in this question, i come up with two unknowns and only one equation.

I attempted this question, i myself am reviewing for my standardized year-end tests..

though I am not sure it is correct.

i stated that:

$$F_{engine} = F_{net} + F_F - F_x$$

Where Fx and Fy are the components of the gravitational force on the object.

After substitution:

$$F_{engine} = ma + \mu mg \cdot cos\Theta - mg \cdot sin\Theta$$

Then i took the mass as the common factor:

$$F_{engine} = m\left( a + \mu g \cdot cos\Theta - g \cdot sin\Theta\right)$$

And then i solve:
$$F_{engine} = m\left( (0.60)(9.8) + (0.28)(9.8)(cos(30)) - (9.8)(sin(30))\right)$$

i end up with $$F_{engine} = 3.37 \cdot m$$ Newtons

which is as much as i could simplify, i don't think you can fully solve this question without the mass.. am i correct?

yes, unless the acceleration could be provided by gravity itself:

i.e sin(a) - u cos(a) = 0.6 Your answer is in agreemnet with that in the book according to the OP.

## 1. What is frictional force and why is it important to calculate?

Frictional force is the force that opposes the movement of an object when it is in contact with another surface. It is important to calculate because it affects the motion and stability of objects and can help us understand and predict how objects will behave in different situations.

## 2. Can frictional force be calculated without knowing the mass of an object?

Yes, frictional force can be calculated without knowing the mass of an object. The formula for calculating frictional force is μN, where μ is the coefficient of friction and N is the normal force. Mass is not a factor in this formula.

## 3. How do you determine the coefficient of friction without knowing the mass?

The coefficient of friction can be determined by conducting an experiment where the normal force and the frictional force are measured. The coefficient of friction can then be calculated by dividing the frictional force by the normal force.

## 4. What are some factors that can affect the magnitude of frictional force?

The magnitude of frictional force can be affected by the smoothness of the surfaces in contact, the force pressing the surfaces together (normal force), and the type of material the surfaces are made of. Additionally, the presence of lubricants or other substances between the surfaces can also affect the frictional force.

## 5. Can the direction of frictional force change without a change in mass?

Yes, the direction of frictional force can change without a change in mass. Frictional force always acts in the opposite direction of the movement or attempted movement of an object, so if the direction of motion changes, the direction of frictional force will also change.

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