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polet [3.4K]
3 years ago
12

An ice cube of mass 50.0 g can slide without friction up and down a 25.0 degree slope. The ice cube is pressed against a spring

at the bottom of the slope, compressing the spring 0.100 m . The spring constant is 25.0 N/m . When the ice cube is released, how far will it travel up the slope before reversing direction? Express your answer numerically in meters to three significant figures. d = nothing m
Physics
1 answer:
lozanna [386]3 years ago
8 0

Answer:

0.6 m

Explanation:

When a spring is compressed it stores potential energy. This energy is:

Ep = 1/2 * k * x^2

Being x the distance it compressed/stretched.

When the spring bounces the ice cube back it will transfer that energy to the cube, it will raise up the slope, reaching a high point where it will have a speed of zero and a potential energy equal to what the spring gave it.

The potential energy of the ice cube is:

Ep = m * g * h

This is vertical height and is related to the distance up the slope by:

sin(a) = h/d

h = sin(a) * d

Replacing:

Ep = m * g * sin(a) * d

Equating both potential energies:

1/2 * k * x^2 = m * g * sin(a) * d

d = (1/2 * k * x^2) / (m * g * sin(a))

d= (1/2 * 25 * 0.1^2) / (0.05 * 9.81 * sin(25)) = 0.6 m

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The terminals of a battery are connected across two resistors in series. The resistances of the resistors are not the same. Whic
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Answer:

(c) The current in each resistor is the same.

Explanation:

When two resistors are connected in series, we have the following:

- The resistors are connected such that the current passing through the two resistors is the same

- The voltage of the battery is equal to the sum of the voltage drops across each resistor

- the equivalent resistance of the circuit is equal to the sum of the individual resistances:

R = R1 + R2

So, let's analyze each statement:

(a) The resistor with the smaller resistance carries more current than the other resistor. --> FALSE. The current through the two resistors is the same.

(b) The resistor with the larger resistance carries less current than the other resistor. --> FALSE. The current through the two resistors is the same.

(c) The current in each resistor is the same. --> TRUE.

(d) The potential difference across each resistor is the same. --> FALSE: the potential difference across each resistor is given by

V=RI

where I (the current) is the same for both resistors, while R (the resistance) is not, so V is also different for the two resistors.

(e) The potential difference is greatest across the resistor closest to the positive terminal --> FALSE. According to

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the potential difference depends only on the value of the resistance, so it doesn't matter which resistor is connected to the positive terminal.

4 0
2 years ago
A cyclotron is to accelerate protons to an energy of 5.4 MeV. The superconduction electromagnet of the cyclotron produces a 2.9T
mart [117]
<h3><u>Answer;</u></h3>

Radius = 0.0818 m

Angular velocity = 2.775 × 10^7 rad/sec

<h3><u>Explanation;</u></h3>

The mass of proton m=1.6748 × 10^-27 kg;  

Charge of electron e= 1.602 × 10^-19 C;  

kinetic energy E= 2.7 MeV

                          = 2.7 × 10^6 × 1.602 × 10^-19 J;

                          = 4.32 × 10^-13 Joules

But; K.E =0.5m*v^2,

Hence v=√(2K.E/m)

Velocity = 2.27 × 10^7 m/s

Angular velocity, ω = v/r

Therefore; V = ωr

Hence; V = √(2K.E/m) = ωr

r= √(2E/m)/w = √E*√(2*m)/(eB)

  = √E * √(2×1.6748×10^-27)/(1.602×10^-19 ×2.9)

but E =  4.32 × 10^-13 Joules

  r = 0.0818 m

Angular speed

Angular velocity, ω = v/r , where r is the radius and v is the velocity

Therefore;

Angular velocity = 2.27 × 10^7 / 0.0818 m

                            = 2.775 × 10^7 rad /sec

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