Question

Конькобежец массой 60 кг толкает камень массой 3 кг в горизонтальном направлении со скоростью 8м/с. На какое расстояние он при этом откатывается, если сила трения коньков о лед составляет 0.02 веса конькобежца.

Answer 1

M1^V1=m2*V2
V2=m1*V1/m2=3*8/60=0,4 м/с
a=k*m2*g/m2=k*g
S=V2^2/2*k*g=0,16/2*0,02*10=0,4 м

Answer 2

Calculation of the Distance the Skater Moves Backward

To calculate the distance the skater moves backward when pushing a stone, we need to consider the force of friction between the skates and the ice.

Given: - Mass of the skater (m1) = 60 kg - Mass of the stone (m2) = 3 kg - Initial velocity of the stone (v) = 8 m/s - Coefficient of friction between the skates and the ice (μ) = 0.02 (as a fraction of the skater's weight)

We can use the principle of conservation of momentum to solve this problem. The initial momentum of the system (skater + stone) is equal to the final momentum of the system.

The initial momentum (p_initial) is given by the sum of the individual momenta of the skater and the stone:

p_initial = m1 * v1 + m2 * v2

Since the skater is initially at rest, the initial velocity of the skater (v1) is 0. Therefore, the initial momentum simplifies to:

p_initial = m2 * v2

The final momentum (p_final) is given by the sum of the individual momenta of the skater and the stone after the skater pushes the stone:

p_final = m1 * v1' + m2 * v2'

Since the stone is pushed horizontally, its final velocity (v2') is also horizontal. The skater moves backward, so the final velocity of the skater (v1') is negative.

Using the principle of conservation of momentum, we have:

p_initial = p_final

m2 * v2 = m1 * v1' + m2 * v2'

Rearranging the equation, we can solve for the final velocity of the skater (v1'):

v1' = (m2 * v2 - m2 * v2') / m1

Now, we can calculate the distance the skater moves backward using the equation for work done by friction:

Work = Force * Distance

The force of friction (F_friction) is given by:

F_friction = μ * m1 * g

where g is the acceleration due to gravity.

The work done by friction is equal to the change in kinetic energy of the skater:

Work = ΔKE

Since the skater starts from rest, the initial kinetic energy (KE_initial) is 0. The final kinetic energy (KE_final) is given by:

KE_final = (1/2) * m1 * (v1')^2

Setting the work done by friction equal to the change in kinetic energy, we have:

μ * m1 * g * d = (1/2) * m1 * (v1')^2

Simplifying the equation, we can solve for the distance (d) the skater moves backward:

d = [(1/2) * (v1')^2] / (μ * g)

Now, let's substitute the given values into the equations and calculate the distance.

Calculation:

Given values: - m1 = 60 kg (mass of the skater) - m2 = 3 kg (mass of the stone) - v = 8 m/s (initial velocity of the stone) - μ = 0.02 (coefficient of friction between the skates and the ice)

Using the equation for the final velocity of the skater (v1'):

v1' = (m2 * v2 - m2 * v2') / m1

Since the stone is initially at rest (v2 = 0), the equation simplifies to:

v1' = -m2 * v2' / m1

Substituting the given values:

v1' = -3 kg * 8 m/s / 60 kg

Calculating the value of v1':

v1' = -0.4 m/s

Using the equation for the distance (d) the skater moves backward:

d = [(1/2) * (v1')^2] / (μ * g)

Substituting the given values:

d = [(1/2) * (-0.4 m/s)^2] / (0.02 * 9.8 m/s^2)

Calculating the value of d:

d ≈ 0.0816 m

Answer:

The skater moves backward by approximately 0.0816 meters when pushing the stone.