Answer:
69.28 m/s
Explanation:
From the question given above, the following data were obtained:
Power = 400 Watt
Time (t) = 10 minutes
Mass (m) = 100 Kg
Velocity (v) =?
Next, we shall convert 10 mins to seconds (s). This can be obtained as follow:
1 min = 60 s
Therefore,
10 mins = 10 × 60
10 mins = 600 s
Next, we shall determine the energy. This can be obtained as follow:
Power = 400 Watt
Time (t) = 600 s
Energy (E) =?
E = Pt
E = 400 × 600
E = 240000 J
Finally, we shall determine how fast the cart is moving. This can be obtained as illustrated below:
Mass (m) = 100 Kg
Energy (E) = Kinetic energy (KE) = 240000 J
Velocity (v) =?
KE = ½mv²
240000 = ½ × 100 × v²
240000 = 50 × v²
Divide both side by 50
v² = 240000 / 50
v² = 4800
Take the square root of both side
v = √4800
v = 69.28 m/s
Thus, the cart is moving with a speed of 69.28 m/s
Measuring mass with a balance
Acceleration is the rate of change of the velocity of a moving object. To determine the speed the object has at a certain time, we need to determine the acceleration first by dividing the speed with the time given. We do as follows:
acceleration = 4.9 m/s / 5.1 s = 0.96 m/s^2
To determine the velocity after 7.1 s, we multiply 7.1 s to the acceleration.
speed or velocity = 0.96 x 7.1 = 6.52 m/s
Answer:
Explanation:
Let m and e are the mass and charge of an electron. It is accelerated from rest through a potential difference V and are then deflected by a magnetic field that is perpendicular to their velocity. Let v is the velocity of the electron. It can be calculated as :
When the electron enters the magnetic field, the centripetal force is balanced by the magnetic force as :
or
So, the radius of the resulting electron trajectory is 
. Hence, this is the required solution.
Answer:
0.21%
Explanation:
We are given;
Mass; m = 100 kg
Diameter; d = 2.2 mm = 2.2 × 10^(-3) m
Young's modulus; E = 12.5 x 10^(10) N/m².
Formula for area is;
A = πd²/4
A = (π/4) x (2.2 x 10^(-3))²
A = 3.8 x 10^(-6) m²
Force; F = mg
g is acceleration due to gravity and has a constant value of 9.8 m/s²
F = 100 × 9.8
F = 980 N
Formula for young's modulus is;
E = Stress/strain
Formula for stress = F/A
Formula for strain = ΔL/L
Thus;
E = (F/A)/(ΔL/L)
Making ΔL/L the subject, we have;
ΔL/L = (F/A)/E
Plugging in the relevant values;
ΔL/L = 980/(3.8 x 10^(-6) × 12.5 × 10^(10))
ΔL/L = 0.0021
Then percentage increase in length of a wire = 0.0021 × 100% = 0.21%
