Answer: F = 131.7N
Explanation:
You are given the following parameters.
Mass M = 30 kg
Coefficient of static friction μ = 0.5
Ø = 30 degrees
When the person is trying to drag the box with force F, the static frictional force Fs will be acting in the opposite direction.
From the figure attached, resolve all forces into horizontal component and vertical component.
Horizontal component:
Fs - F cosØ = 0
Fs = F cosØ
F cosØ = μN ...... (1)
Vertical component:
N + F SinØ - mg = 0
N = Mg - F SinØ ..... (2)
Substitutes m, g and Ø into the equation 2
N = (30 × 9.8) - F × sin30
N = 294 - 0.5F
Substitute N and coefficient of friction into the equation (1)
F cos30 = 0.5 (294 - 0.5F)
Open the bracket
0.8660F = 147 - 0.25F
Collect the like terms
1.116025F = 147
F = 147/1.116025
F = 131.7 N
Therefore, the minimum force the person needs to have to move the box along the floor is 131.7 N
Gravity is the force that pulls us to the surface of the Earth, keeps the planets in orbit around the Sun and causes the formation of planets, stars and galaxies.
Answer:
The slower runner is 1.71 km from the finish line when the fastest runner finishes the race.
Explanation:
Given;
the speed of the slower runner, u₁ = 11.8 km/hr
the speed of the fastest runner, u₂ = 15 km/hr
distance, d = 8 km
The time when the fastest runner finishes the race is given by;
The distance covered by the slower runner at this time is given by;
d₁ = u₁ x 0.533 hr
d₁ = 11.8 km/hr x 0.533 hr
d₁ = 6.29 km
Additional distance (x) the slower runner need to finish is given by;
6.29 km + x = 8km
x = 8 k m - 6.29 km
x = 1.71 km
Therefore, the slower runner is 1.71 km from the finish line when the fastest runner finishes the race.