what is the minimum amount of force that must be applied to the sled in order to start it moving? the static friction is 0.30 and the sliding coefficient is 0.10 and the total mass of the sled is 50 kg

Where is the sled? On a hill? it matters.

To determine the minimum amount of force required to start the sled moving, we need to consider the forces acting on the sled. In this case, we have two types of friction: static friction and sliding friction.

1. Static Friction (fs):
Static friction is the force that opposes the initial motion of an object at rest. The maximum static friction force can be calculated using the equation:

fs = μs * N

where μs is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the weight of the sled, which can be calculated as:

N = m * g

where m is the mass of the sled and g is the acceleration due to gravity (9.8 m/s^2).

2. Sliding Friction (fk):
Once the sled starts moving, the friction changes to sliding friction. The sliding friction force can be calculated using the equation:

fk = μk * N

where μk is the coefficient of sliding friction and N is the normal force (same as before).

3. Minimum Force (Fmin):
The minimum force required to start the sled moving is equal to the maximum static friction force. Therefore:

Fmin = fs

Now let's calculate the minimum force needed to start the sled:

Given:
μs (coefficient of static friction) = 0.30
m (mass of the sled) = 50 kg

Step 1: Calculate the normal force (N):
N = m * g
= 50 kg * 9.8 m/s^2
= 490 N

Step 2: Calculate the maximum static friction force (fs):
fs = μs * N
= 0.30 * 490 N
= 147 N

Step 3: Calculate the minimum force needed to start the sled (Fmin):
Fmin = fs
= 147 N

Therefore, the minimum amount of force that must be applied to the sled in order to start it moving is 147 Newtons.