Physics, 04.10.2019 23:30 alexamorantess

You are going sledding with your friends, sliding down a snowy hill. friction can't be ignored. riding solo on your sled, you have a certain acceleration. would the acceleration change if you let a friend ride with you, increasing the mass?

yes, increasing the mass does increase the inertia. a=fnetm. since the mass is increased, the acceleration decreases.
no, increasing the mass does increase the net force on the system, but it also increases the inertia. a=fnetm. since both the net force and mass are increased they still cancel, leaving the acceleration the same.
no, increasing the mass does increase the net force on the system, but it also increases the inertia. a=mfnet. since both the net force and mass are increased they still cancel, leaving the acceleration the same.
yes, increasing the mass does increase the net force on the system. a=fnetm. since the net force is increased, the acceleration increases too.

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If you let a friend ride with you, increasing the mass does increase the net force on the system, but it also increases the inertia. a=Fnetm. Since both the net force and mass are increased they still cancel, leaving the acceleration the same.

Further explanation

Inertia is the tendancy of a moving object to keep moving in a straight line or of any object to resist a change in motion.

According to the picture below, we choose x-direction parallel to the inclined surface. Our positive direction is to the right. Hence, we will calculate the acceleration when riding solo first:

$\Sigma F_x = mg sin \theta - F_k = m a_x\\mg sin \theta - F_k = m a_x\\a_x = \frac{mg sin \theta - F_k }{m} ... (1)\\$

$\Sigma F_y = F_n - mg cos \theta = m a_y = 0\\F_n = mg cos \theta\\F_k = \mu_k F_n\\F_k = \mu_k mg cos \theta\\$

Put (2) into (1)

$a = \frac{m g sin \theta - \mu_k m g cos \theta}{m} \\a = g sin \theta - \mu_k g cos \theta$

From the equation 3, we found that the acceleration does not depend on the mass of the object. Notice that:

is constant

$\theta$ is constant,

$\mu_k$ is constant

So that, is constant whatever the amount of the mass is

Learn moreLearn more about inertia Answer details

Grade: 9

Subject: physics

Chapter: inertia

Keywords: inertia

Answer from: musicaljay1276

The acceleration of the two friends sliding will not change as acceleration does not depend on mass.

Further explanation:

When a person is sliding on a sled it experiences friction which helps in accelerating the sled. If one more person is added to the sled then the acceleration of the sled does not change.

Concept used:

Consider an inclined snowy hill on which sled is sliding.

Friction force is defined as the opposing force acting in the opposite direction of the motion of the body.

The expression for the friction force is given as.

${F_{\text{k}}} = {\mu _{\text{k}}}N$ …… (1)

Here, ${\mu _k}$ is the coefficient of friction.

Normal component of the person is balanced by the cosine component of weight.

$N = mg\cos \theta$

Substitute $mg\cos \theta$ for in equation (1).

${F_{\text{k}}} = {\mu _{\text{k}}}\left( {mg\cos \theta } \right)$

Net force of the person is given as.

${F_{{\text{net}}}} = ma$ …… (2)

The expression for the net force as balanced by the forces is given as.

${F_{net}}= mg\sin \theta-{\mu _{\text{k}}}\left( {mg\cos \theta } \right)$

The final expression reduces as.

${F_{net}} = mg\left( {\sin \theta- {\mu _{\text{k}}}\cos \theta } \right)$ …… (3)

On comparing equation (2) and (3).

$\fbox{\begin\\a = g\left( {\sin \theta- {\mu _{\text{k}}}\cos \theta } \right)\end{minispace}}$ …… (4)

The expression for the net force when two people are sliding on a single sled.

${F_{{\text{net}}}} = \left( {m + M} \right)a$

The resultant force expression is given as.

${F_{net}} = \left( {m + M} \right)g\left( {\sin \theta- {\mu _{\text{k}}}\cos \theta } \right)$

Equating the above two expressions we get.

$\fbox{\begin\\a = g\left( {\sin \theta- {\mu _{\text{k}}}\cos \theta} \right)\end{minispace}}$ …… (5)

On comparing equation (4) and (5) we came to know that both the accelerations are same. Above expression shows that acceleration is independent of mass of the body.

Thus, when two friends will slide on the same sled the acceleration remain unchanged because as mass increases force also increases that balances each other.

Learn more:

1. Net force on a body .

2. Conservation of momentum .

3. Motion of a block under friction .

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

Acceleration, force, acceleration due to gravity, friction, normal, weight, mass, motion, sliding, sled, hill, inclined, plane, coefficient of friction, angle of inclination.

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