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a) Average power: 1425 W
b) Instantaneous power at 3.0 seconds: 2850 W
Given that the object moves along the ramp with uniform acceleration due to a constant force, we can apply the suvat equation:
s = 18 m (the distance covered along the ramp)
u = 0 (initial speed)
t = 3.0 s (time taken)
a is the acceleration of the object along the ramp
Calculating the acceleration 'a' using this data,
Next, we use Newton's second law to determine the net force acting on the object:
This net force consists of the applied force acting forward and the backward component of weight, allowing us to calculate the applied force.
m = 24 kg (mass of the object)
Now, we can compute the work done by the applied force, which runs parallel to the ramp:
s = 18 m (displacement)
The average power required is thus determined.
b) The instantaneous power at any point during the motion can be calculated using:
where F is the force applied and v is the object's velocity.
With the previously calculated applied force, as this is uniformly accelerated motion, we can also find the velocity at the end of the 3.0 seconds using the suvat equation:
It shows a situation where a proton moves perpendicular to a magnetic field of 0.025 tesla. The force acting on the proton has a magnitude of 1.8 × 10⁻¹⁴ newtons, and we need to determine the speed of the proton given q = 1.6 × 10⁻¹⁹ coulombs.
Answer:
Explanation:
Considering that,
The mass of the first vehicle
M1= 328kg
It is traveling in the positive x direction at a speed of
U1 = 19.1m/s
The speed of the second vehicle
U2 = 13m/s, moving in the same direction as the first vehicle..
The mass of the second vehicle
M2 = 790kg
The speed of the second vehicle post-collision
V2 = 15.1 m/s
The speed of the first vehicle following the collision
V1 =?
This represents an elastic collision,
and applying the principle of conservation of momentum
The momentum prior to the collision must equal the momentum afterwards
P(before) = P(after)
M1•U1 + M2•U2 = M1•V1 + M2•V2
328 × 19.1 + 790 × 13 = 328 × V1 + 790 × 15.1
16534.8 = 328•V1 + 11929
328•V1 = 16534.8—11929
328•V1 = 4605.8
V1 = 4605.8/328
V1 = 14.04 m/s
The speed of the first vehicle after the collision is 14.04 m/s
Answer:
2023857702.507 m
Explanation:
Using Newton's law of gravitation:
G = gravitational constant
m_shrew = 50 g
m_elephant = 5 × 10^3 kg
r_earth = Earth's radius, 6400 km or 6,400,000 m
m_earth = Earth's mass
Equate the gravitational forces:
G m_shrew m_earth / r_earth^2 = G m_elephant m_earth / r^2
Cancel common terms on both sides:
m_shrew / r_earth^2 = m_elephant / r^2
Rearranged to solve for r^2:
r^2 = (m_elephant × r_earth^2) / m_shrew
Substituting the values:
r^2 = 4.096 × 10^{13}
Taking square root gives:
r = 2,023,857,702.507 m
