During a football game, a receiver has just caught a pass and is standing still. Before he can move, a tackler, running at a vel
1 answer:
You might be interested in
Answer:
ΔK = -6 10⁴ J
Explanation:
This is a crash problem, let's start by defining a system formed by the two trucks, so that the forces during the crash have been internal and the moment is preserved
initial instant. Before the crash
p₀ = m v₁ + M 0
final instant. Right after the crash
p_f = (m + M) v
p₀ = p_f
mv₁ = (m + M) v
v =
we substitute
v = 3
v = 1.0 m / s
having the initial and final velocities, let's find the kinetic energy
K₀ = ½ m v₁² + 0
K₀ = ½ 20 10³ 3²
K₀ = 9 10⁴ J
K_f = ½ (m + M) v²
K_f = ½ (20 +40) 10³ 1²
K_f = 3 10⁴ J
the change in energy is
ΔK = K_f - K₀
ΔK = (3 - 9) 10⁴
ΔK = -6 10⁴ J
The negative sign indicates that the energy is ranked in another type of energy
Answer:
A) v₁ = 10.1 m/s t₁= 4.0 s
B) x₂= 17.2 m
C) v₂=7.1 m/s
D) x₂=7.5 m
Explanation:
A)
- Assuming no friction, total mechanical energy must keep constant, so the following is always true:
- Choosing the ground level as our zero reference level, Uf =0.
- Since the child starts from rest, K₀ = 0.
- From (1), ΔU becomes:
- In the same way, ΔK becomes:
- Replacing (2) and (3) in (1), and simplifying, we get:
- In order to find v₁, we need first to find h, the height of the slide.
- From the definition of sine of an angle, taking the slide as a right triangle, we can find the height h, knowing the distance that the child slides down the slope, x₁, as follows:
Replacing (5) in (4) and solving for v₁, we get:
- As this speed is achieved when all the energy is kinetic, i.e. at the bottom of the first slide, this is the answer we were looking for.
- Now, in order to finish A) we need to find the time that the child used to reach to that point, since she started to slide at the its top.
- We can do this in more than one way, but a very simple one is using kinematic equations.
- If we assume that the acceleration is constant (which is true due the child is only accelerated by gravity), we can use the following equation:
- Since v₀ = 0 (the child starts from rest) we can solve for a:
- Since v₀ = 0, applying the definition of acceleration, if we choose t₀=0, we can find t as follows:
B)
- Since we know the initial speed for this part, the acceleration, and the time, we can use the kinematic equation for displacement, as follows:
- Replacing the values of v₁ = 10.1 m/s, t₂= 2.0s and a₂=-1.5m/s2 in (10):
C)
- From (6) and (8), applying the definition for acceleration, we can find the speed of the child whem she started up the second slope, as follows:
D)
- Assuming no friction, all the kinetic energy when she started to go up the second slope, becomes gravitational potential energy when she reaches to the maximum height (her speed becomes zero at that point), so we can write the following equation:
- Replacing from (12) in (13), we can solve for h₂:
- Since we know that the slide makes an angle of 20º with the horizontal, we can find the distance traveled up the slope applying the definition of sine of an angle, as follows: