A sled rests at the top of a 25 degree slope that is 80m in length. If uk = .25 and the velocity at the bottom of the incline is 20m/s then what is the weight of the sled?
Potential energy loss going down = M*g*80 sin 25 = 331.3 M
Kinetic energy acquired going down = (1/2) M*(Vfinal)^2 = 200.0 M
Work done against friction going down =
M*g*cos25*80*uk = 177.6 M
The first number must equal the sum of the last two numbers. There is no value of mass M that works.
To find the weight of the sled, we need to use the equation:
Weight = mass * gravitational acceleration (g)
First, let's find the mass of the sled. We can use the equation:
Weight = mass * gravitational acceleration (g)
Weight = mass * 9.8 m/s^2
Now let's find the gravitational force acting on the sled. The gravitational force is equal to the weight of the sled:
Gravitational force = Weight of the sled
The gravitational force can be calculated using the equation:
Gravitational force = Mass * Acceleration due to gravity (g)
The acceleration (a) of the sled can be determined using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
In this case, the force acting on the sled is the gravitational force going down the incline and the frictional force opposing the sled's motion. The frictional force can be calculated using the equation:
Frictional force = coefficient of kinetic friction (μk) * Normal force (N)
The normal force (N) can be determined by resolving the forces along the incline:
Normal force (N) = Weight of the sled * cos(theta)
where theta is the angle of the slope (25 degrees).
Once we find the normal force, we can calculate the frictional force:
Frictional force = coefficient of kinetic friction (μk) * Normal force (N)
Now, let's calculate the net force acting on the sled:
Net force (Fnet) = Gravitational force - Frictional force
The net force is also equal to the product of the mass and acceleration of the sled:
Net force (Fnet) = mass * acceleration (a)
Since we know the acceleration (a) of the sled is zero (it's at rest), we can set up the equation:
Net force (Fnet) = 0
Equating the above two equations, we get:
0 = Gravitational force - Frictional force
Now, we can substitute the derived equations into this equation to find the weight of the sled.